Photoelectrons are emitted from two similar metal plates when wavelengths λ 1 and λ 2 are incident on them ( λ 1 = 1.5 λ 2 ). If maximum kinetic energy of emitted photoelectrons is E 1 and E

Question

Photoelectrons are emitted from two similar metal plates when wavelengths λ 1 ​ and λ 2 ​ are incident on them ( λ 1 ​ = 1.5 λ 2 ​ ). If maximum kinetic energy of emitted photoelectrons is E 1 ​ and E 2 ​ respectively then

TestHub · Accepted Answer

Using Einstein's photoelectric equation:

$E_{1} = \frac{h c}{λ _{1}} - ϕ$

$E_{2} = \frac{h c}{λ _{2}} - ϕ$

Given $λ_{1} = 1.5 λ_{2} = \frac{3}{2} λ_{2}$ , we can write:

$E_{1} = \frac{2 h c}{3 λ _{2}} - ϕ$

From the second equation, $\frac{h c}{λ _{2}} = E_{2} + ϕ$ . Substituting this into the equation for $E_{1}$ :

$E_{1} = \frac{2}{3} (E_{2} + ϕ) - ϕ$

$E_{1} = \frac{2}{3} E_{2} - \frac{1}{3} ϕ$

Since the work function $ϕ > 0$ , it follows that:

$E_{1} < \frac{2}{3} E_{2}$

Answer: $E_{1} < 2 E_{2} /3$

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